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Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 43796, 9 pages
http://dx.doi.org/10.1155/JAMSA/2006/43796

Random fixed point theorems for multivalued nonexpansive non-self-random operators

1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand

Received 8 March 2005; Revised 9 June 2005; Accepted 4 August 2005

Copyright © 2006 S. Plubtieng and P. Kumam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let (Ω,Σ) be a measurable space, with Σ a sigma-algebra of subset of Ω, and let C be a nonempty bounded closed convex separable subset of a Banach space X, whose characteristic of noncompact convexity is less than 1, KC(X) the family of all compact convex subsets of X. We prove that a multivalued nonexpansive non-self-random operator T:Ω×CKC(X), 1-χ-contractive mapping, satisfying an inwardness condition has a random fixed point.